The present disclosure relates to resonators, and more particularly to resonators suitable for continuous-time oversampling ΔΣ converters.
Oversampling A/D converters are widely used for front ends of communication devices and conversion of audio signals, and are essential circuit techniques for present communication, video, and audio signal processing circuits. As a type of oversampling A/D converters, there are continuous-time delta sigma A/D converters (CTDS-ADCs) including continuous-time filters such as integrators and resonators.
In a conventional CTDS-ADC, an input signal passes through a number n of cascade-coupled continuous-time filters, and is quantized by a quantizer. A digital output of the quantizer is converted to analog current signals by a number n of D/A converters, and then fed back to the respective number n of continuous-time filters. Since CTDS-ADCs do not include any switch in an analog circuit, voltages can be lowered. Moreover, CTDS-ADCs do not require any prefilter which is usually needed when using a sampling filter. In these respects, CTDS-ADCs are suited for application of communication systems, and the application has been increasingly researched and developed in recent years.
In order to improve resolution performance and SN characteristics of CTDS-ADCs, the order of a quantization noise transfer function needs to be increased. However, numbers of operational amplifiers are needed to achieve high-order transfer characteristics, thereby causing disadvantages in a circuit size and power consumption. Thus, realization of high-order transfer characteristics with a few operational amplifiers is required. As an example, there is a resonator as shown in FIG. 9, which achieves second-order transfer characteristics with a single operational amplifier. This resonator includes a twin T notch filter between an output terminal and an inverting input terminal of an operational amplifier 10. A signal Vin is input to the inverting input terminal of the operational amplifier 10 via a resistive element Rin, and a signal Vout is output from the output terminal of the operational amplifier 10. The twin T notch filter includes a first T filter having resistive elements 11 and 12, and a capacitive element 23, and a second T filter having capacitive elements 21 and 22, and a resistive element 13 (see, e.g., Japanese Patent Publication No. H03-216559). Since a signal is not fed back from the output terminal to a non-inverting input terminal of the operational amplifier 10 at a resonance frequency of the twin T notch filter, a feedback loop of the operational amplifier 10 is substantially open, thereby obtaining extremely high gain. On the other hand, although it is not a resonator, a second-order filter is known, in which a signal is input not to an inverting input terminal of an operational amplifier but to an intermediate node between a first and second T filters (see, e.g., U.S. Pat. No. 4,553,103).
In the above-mentioned second-order resonator, where resistance values of the resistive elements 11-13 are R1, R2, and R3, and capacitance values of the capacitive elements 21-23 are C1, C2, and C3, respectively, the resonance condition is represented as follows.1/R3=1/R1+1/R2 and C3=C1+C2 A transfer function is represented by the following equation. Note that s is the Laplace operator.
                              Vout          Vin                =                  -                                                                                          (                                                                  1                                                  C                          1                                                                    +                                              1                                                  C                          2                                                                                      )                                                        -                    1                                                  ⁢                s                            +                                                                    1                                          R                      1                                                        +                                      1                                          R                      2                                                                                                            C                    1                                    ⁢                                      C                    2                                                                                                      s                2                            +                              Rin                                                      R                    1                                    ⁢                                      R                    2                                    ⁢                                      C                    1                                    ⁢                                      C                    2                                                                                                          Equation        ⁢                                  ⁢        1            
In the transfer function, the capacitance value C1 and the capacitance value C2 are included in all of the first-order and zeroth-order coefficients of the numerator, and the zeroth-order coefficient of the denominator. Thus, when at least one of the capacitance value C1 and the capacitance value C2 is changed to change the first-order term of s, the pole frequency and the zeroth-order term of s change at the same time. As such, in a conventional second-order resonator, coefficients of the transfer function are associated with each other, and thus, great design efforts are needed to realize desired transfer characteristics. It is also difficult to dynamically change the transfer characteristics to desired values in accordance with the type of application.